I used to be a carer and this was a constant consideration for me, as our uniform also dictated my arms had to be bare at all times.
It's sort of unavoidable that some people will notice, and in my experience one of three things can happen, which you should prepare yourself for;
1. They may or may not have noticed, but you won't know because they say nothing. You have no way of telling if they've noticed, or what they're thinking/feeling if they have, so simply carry out your duties to the best of your ability and don't worry yourself.
2. They notice but don't understand what your scars signify - these people tend to ask "Ooh what did you do there?" or "what's all this?" It's best to have a rehearsed response ready, but what response you give is up to you.You can be as honest as you feel is appropriate.
3. They respond badly. This is a vague umbrella term for numerous responses you might get, and I'm afraid there's not much you can do to avoid all the ignorant patients. All you can do is reassure them that you know what you're doing and do your job as well as you can.
Is there a line manager or someone you can discuss this with?
In my experience most people notice scars but don't mention them.